Wire electro discharge machining (WEDM) is one of the most productive non-traditional machining processes. Complex shapes can be cut through the WEDM process. In the present study, attempts have been made to study the effects of various process parameters of WEDM such as pulse on time (T on), pulse off time (T off), servo voltage (SV), wire speed (WS) and servo feed (SF) on the material removal rate (MRR) and surface roughness (SR) for machining of TiNiCo shape memory alloys, traditionally used as bone staple material. Grey-relational-analysis-based entropy measurement methods were used for formulating a hybrid combination of optimisation methods, in order to investigate the input parameters of WEDM on the comprehensive performance of a bone staple material’s SR and MRR. Experiments were carried out by using response surface design (L-33), and the input parameters were ranked based on the grey relational grade. An experimental run was conducted using the optimal combination of input parameters of WEDM, which was obtained from the analysis. T on of 125 μs, T off of 42 μs, SV of 40 V, SF of 2180 machine units and WS of 4 m/min were obtained as the best combination of input process parameters for TiNiCo alloy.